# How do you write an equation for the line that passes through (4,7) and is perpendicular to the line y=2/3x-1?

Oct 21, 2016

Please see the explanation for the process. $y = - \frac{3}{2} x + 19$

#### Explanation:

The slope of the line: $y = \frac{2}{3} x - 1$ is $\frac{2}{3}$.

The slope of any line perpendicular is the negative reciprocal: $- \frac{3}{2}$

Use the point-slope form of the equation of a line to force the line through point $\left(4 , 7\right)$:

$y - 7 = - \frac{3}{2} \left(x - 4\right)$

$y - 7 = - \frac{3}{2} x + 12$

$y = - \frac{3}{2} x + 19$